Theorem ancl 567

Description: Conjoin antecedent to left of consequent. (Contributed by NM, 15-Aug-1994.)

Assertion

Ref	Expression
ancl	⊢ ((𝜑 → 𝜓) → (𝜑 → (𝜑 ∧ 𝜓)))

Proof of Theorem ancl

Step	Hyp	Ref	Expression
1		pm3.2 462	. 2 ⊢ (𝜑 → (𝜓 → (𝜑 ∧ 𝜓)))
2	1	a2i 14	1 ⊢ ((𝜑 → 𝜓) → (𝜑 → (𝜑 ∧ 𝜓)))

Syntax hints:   → wi 4   ∧ wa 383

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This theorem depends on definitions:  df-bi 196  df-an 385

This theorem is referenced by:  bnj1118  30306  bnj1128  30312  bnj1145  30315  bnj1174  30325